How to fix the rig after weight painting
Every IK constraints has a "chain lenght" parameter, setting the amount of bones involved in the IK solution: 1 means that only the constrainted bone will try to reach the target, 2 means that the constrained bone and its first neighbour will act as an IK chain, and so on. 0 means that every connected bone will be part of the chain. 

In your screenshot it looks like the Right forearm has a 0 chain, propagating the IK action until the neck-clavicle junction, while every IK should be set to 1 chain lenght.

Consider also that - generally - we use a single IK constraint to control forearm and upper arm bones, with an addictional bone named "pole" to control the elbow position: this is the "standard" method!